I am considering changing my computer from Windows XP to Ubuntu, but I want to be able to read my Openoffice documents without a lot of hassle. Does Libreoffice have this capability?
Depends which file type you use for your documents.
As far I know LibreOffice only removed the import filters for binary StarOffice files (like .swx etc) (see LibreOffice 4.0: Release Notes - The Document Foundation Wiki). ODF, Word (.doc(x)), Excel (.xls(x)), Powerpoint (.ppt(x)), … files will be imported like OpenOffice import it (or better 
).
I hope that’s an answer to your question?
PS: you can always install libreoffice on your XP computer to test it out. (download: http://www.libreoffice.org/download)
Kind regards,
Joren
You can download LibreOffice Portable on Windows as well, just download it and test it before installing…
As @Ljilian pointed already to portable versions. I keep the latest portable version of the 3.6 series because this version can still open very old file formats.